I think this is Daltons Law Problem

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The discussion revolves around calculating the total pressure of a gas mixture from two separate flasks containing oxygen and nitrogen. The initial conditions include a 250 ml flask of oxygen at 150 mmHg and a 500 ml flask of nitrogen at 135 mmHg. The gases are combined into a single volume without temperature change, prompting the use of Dalton's Law of Partial Pressures. The key point is that the pressure of each gas changes when they occupy the combined volume. The final pressure is determined by calculating the contributions of each gas to the new total volume, leading to a total pressure of 140 mmHg. The initial assumption that simply adding the pressures would suffice is corrected by recognizing the need to account for the change in volume for each gas.
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Hi guys, I hope you can help me out with this seemingly simple problem. I honestly tried but I couldn't get any answer:

A 250 ml flask contains oxygen at a pressure of 150 mmHg and another flask contains 500 ml of Nitrogen at a pressure of 135 mmHg. The two flasks were then connected so that each gas filled their combined volumes. Assuming no change in temperature, what is the total pressure of gas in the final mixture?

I think this has to do with Daltons law but I don't know how to solve it.

Why wouldn't P1+P2 give me the answer?
 
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I think I solved the problem. I believe the key to this problem is that when each of the gas enters the new volume, the pressure by each gas changes. Then taking the final pressure contributed by each gas in the new volume, I added those to give me an answer of 140mmHg.
 
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